Harmonic Analysis and Its Applications

Harmonic analysis and its applications is a central, broad, and burgeoning
area on the international mathematical landscape. In the Department of
Mathematics it is represented by the Norbert Wiener Center with its
mission to
develop harmonic analysis in the context of vital industrial technologies,
and,
in turn, to enhance these technologies by virtue of fundamental, deep,
applicable harmonic analysis. The Norbert Wiener Center is the
mathematical
edifice to address Mathematical Engineering in the 21st century. There is
no
doubt that Mathematical Engineering will be to today's mathematics
departments
what Mathematical Physics was to those a century ago.

Whereas Mathematical Physics was an impetus for the study of differential
equations and numerical analysis in mathematics departments of the 20th
century,
the Norbert Wiener Center will provide state of the art research in areas
such
as waveform design for radar and communications, and sigma-delta
quantization
for multifunction systems which are central to next generation government
programs.

The present applicable expertise of the Norbert Wiener Center includes: biomathematics and biomedical engineering, medical imaging and diagnostics, signal and image processing, waveform design, opportunistic sensing, non-uniform sampling, compressed sensing, machine learning, quantum detection, RADAR and SONAR processing, RF communications, dimension reduction, hyperspectral and LIDAR data analysis, and wavelet and time-frequency theory. The Center believes in the importance of continued strong theoretical
underpinnings; and it deals interactively with major industrial and government research laboratories on cutting-edge concepts in Mathematical Engineering.